Erratum: Gross-Pitaevskii equation for Bose particles in a double well potential: Two mode models and beyond [Phys. Rev. A73, 013604 (2006)]

Abstract

In the second quantization section there is an error in the interaction term. Eq. ͑46͒ should read

Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose-Einstein condensates

“…It is not difficult to demonstrate that for slowly changing parameters one can use the same model, with parameters of the Hamiltonian slowly changing in accordance with the "instantaneous" model. For simplicity, let us demonstrate this using the improved 2-mode model [38] as an example. The order parameter in a two-mode approximation is…”

“…where P ± , Q ± are functions of ψ 1 , ψ 2 (see [38]). From these equations, one get the equations of motion for ψ 1 , ψ 2 (Eqs.…”

“…It is worth to mention that for BEC in a symmetric double-well, there exist also improved 2-mode model [38], where the term cos 2φ is added:…”

“…The variables of the classical Hamiltonian are defined as (17) into the time-dependent GP equation, one gets [38] i dψ 1 …”

“…The phenomenon is very important for BEC physics: we consider here nonlinear two-mode models related to tunnelling between coupled BEC in a double well [23], nonlinear Landau-Zener tunnelling [24,25], Feshbach resonance passage in atom-molecule systems [26,27,28]. Nonlinear two-mode models were extensively studied previously (sometimes beyond the mean-field approxima- * Electronic address: alx˙it@yahoo.com tion, [23,24,25,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]), and destruction of adiabaticity was discussed already in [24,25,26], still there are regimes of motion that were not analyzed in these papers from the point of view of nonadiabatic behaviour, that is, when initial populations of both modes are not zero (or very small), but finite. We presented some of our results on that theme in [27,28]; nevertheless destruction of adiabatic invariance has not been studied systematically in BEC-related models yet.…”